Spectra and symmetry in nuclear pairing

Abstract

We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell, there are degeneracies between the states corresponding to less than and more than half full shell. We also provide a technique to solve the equations of Bethe ansatz.